GIFT  or 

A.llen  Knipht 


INDEMNITY   BONDS   FOR    15   OR   20  YEARS 

(including  insurance),  for  from 

$1,000  to  $100,000, 


ARE   ISSUED    BY   THE 


EQUITABLE   LIFE  ASSURANCE   SOCIETY 

OF  THE  UNITED  STATES, 
Payable  at  the  death  of  the  assured,  if  previous  to  their  maturity. 


PAYABLE  FOR  IN  ANNUAL,  SEMI-ANNUAL  OR  QUARTERLY  INSTALMENTS. 


BONDS  PAID  UP  IN  10  YEARS. 


ANNUAL   INSTALMENTS   PER  $1,000. 


20-YEAR  BOND  —  20  ANNUAL  INSTALMENTS. 

IS-YEAR  BOND  —  10  ANNUAL  INSTALMENTS. 

Age  at  issue. 
20  

$50" 
50 
50 
60 
80 

Cash  return  on 
maturity  of  bond 
at  end  of  20  years 
(on  basis  explain- 
ed below),  $1,700. 

Age  at  issue. 
20  

$100 
IOO 
IOO 
IOO 

1  20. 

Cash   return  on 
maturity   of   bond 
at  end  of  15  years 
(on  basis  explain- 
ed below),  between 
$1,300  and  $1,400. 

•30.  . 

"\O.  . 

40  .... 

40.  . 

SO.  . 

SO.  . 

60  

60  

The  exact  amount  of  profits  which  will  be  earned  and  distributed  among  the 
holders  of  such  Indemnity  Bonds  as  become  fully  paid-up  and  then  mature,  cannot  be 
stated  in  advance,  as  they  depend  in  a  measure  upon  varying  quantities,  such  as  the 
rate  of  interest,  mortality  and  expense  ;  but  careful  calculations,  based  on  the  experi- 
ence of  the  Society  up  to  the  present  time,  show  the  surplus  profits  which  would  be 
payable  with  such  bonds  if  they  had  been  issued  by  the  Society  15  or  20  years  ago 
and  matured  to-day.  While  such  figures  can  give  only  an  approximate  idea  of  the 
results  of  the  future,  they  furnish  the  best  attainable  data  upon  which  to  judge  of  the 
value  of  these  Bonds. 


\ 


THE    THIRTIETH  ANNUAL    STATEMENT   OF 

The    Equitable   Life    Assurance    Society 

OF    THE     UNITED    STATES, 

For  the  Year  Ending  December  31,  1889. 


AMOUNT  OF  LEDGER  ASSETS,  JANUARY  i,  1889 ..      $89,427,026.92 

Less  Contingent  Sinking  Fund 600,000.00 

$88,827,026.92 
Incotne. 

Premiums     $25i357i522-75 

Interest,  Rents,  etc Si°35. 765-53         $30,393,288.28 

$119,220,315.20 
Disbu  rsements. 

Claims  by  Death  and  Matured  Endowments $7,878,499.53 

Dividends,  Surrender  Values,  Annuities  and  Discounted  Endowments....  3,964,358.36 

Total  Paid  Policy-holders $11,842,857.89 

Dividend  on  Capital 7,000.00 

Commissions,  Advertising,  Postage  and  Exchange 3,176,239.09 

General  Expenses,  State,  County,  City  Taxes 2,820,855.91         $17,846,952.89 

Net  Ledger  Assets,  December  31,  1889 $101, 373,362.31 

Assets. 

Bonds  and  Mortgages $23,637,873.52 

Real  Estate,  including  the  Equitable  Buildings  and  purchases  under  fore- 
closure of  mortgages 16,536,541.33 

United  States  Stocks,  State  Stocks,  City  Stocks,  in  Trust  Companies  and 

other  Investments 451645,395.63 

Loans  secured  by  Bonds  and  Stocks  (Market  Value,  $3,404,859) 2,705,000.00 

Real  Estate  outside  the  State  of  New  York,  including  purchases  under 

foreclosure  of  mortgages 8,116,755.06 

Cash  in  Banks  and  in  transit  (since  received  and  invested) 3,960,630.63 

Due  from  Agents  on  account  of  Premiums 771,166.14        $101,373,362.31 

Market  value  of  Stocks  and  Bonds  over  book  value 2,697,138.55 

Interest  and  Rents  due  and  accrued 829,895.26 

Premiums  deferred  and  in  transit 2,249,913.00 

Total  Assets,  December  31,  1889 $107,150,309.12 

I  hereby  certify,  that  after  a  personal  examination  of  the  securities  and  accounts 
described  in  this  statement,  I  find  the  same  to  be  true  and  correct  as  stated. 

JOHN  A.  McCALL,  Comptroller. 

Total  Liabilities,  including  legal  reserve  on  all  existing  Policies  (4%  Standard) $84.329,234.9a 

Total  Undivided  Surplus  over  1$  Reserve #22,821,074.20 

Of  which  the  proportion  contributed  (as  computed)  by  Policies  in  general 

class,  is $6,848,611.20 

Of  which  the  proportion  contributed  (as  computed)  by  Policies  in  Tontine 

class,  is .     15,972,463.00 

We  certify  to  the  correctness  of  the  above  calculation  of  the  reserve 

and  surplus.    From  this  surplus  the  usual  dividends  will  be  made.     GEO.  W.  PHILLIPS,  \   Aftua-;f. 

J.G.VANCISE,         fAt****** 

New  Assurance  written  in  1889 $1751264,100 

Total  Outstanding  Assurance $631.016,666 

We,  the  undersigned,  have,  in  person,  carefully  examined  the"  accounts,  and  counted  and  examined  in 
detail  the  assets  of  the  Society,  and  certify  that  the  foregoing  statement  thereof  is  correct. 

BENNINGTON  F.  RANDOLPH,  )  Special  Committee  of  the  Board  of  Directors, 

THOS.  S.  YOUNG,  HENRY  S.  TERBELL,  V     appointed  to  examine  the  accounts  and  as- 

GEORGK  W.  CARLETON,       E.  BOUDINOT  COLT,  )     sets  at  the  close  of  the  year  1889. 


BOARD    OF    DIRECTORS. 

HENRY  B.  HYDE,  PRESIDENT. 
JAMES  W.  ALEXANDER,  VICE-PRESIDENT. 


Louis  FITZGERALD, 
HENRY  A.  HURLBUT, 
HENRY  G.  MARQUAND, 
WM.  A.  WHEELOCK, 
HENRY  DAY, 
M.  HARTLEY, 
H.  M.  ALEXANDER, 
CHAUNCBY  M.  DEPEW, 
CHARLES  G.  LANDON, 
CORNELIUS  N.  BLISS, 
ALANSON  TRASK, 
E.  BOUDINOT  COLT 
EUGENE  KELLY, 


JOHN  D.  JONES, 
JOHN  SLOANE, 
S.  BORROWE, 
B.  WILLIAMSON, 
G.  W.  CARLETON, 
E.  W.  LAMBERT, 
H.  S.  TERBELL, 
THOMAS  S.  YOUNG, 
WILLIAM  M.  BLISS, 
JOHN  J.  McCooK, 
B.  F.  RANDOLPH, 
JOHN  A.  STEWART, 
LEVI  P.  MORTON, 


GEO.  C.  MAGOUN, 
WM.  B.  KENDALL, 
DANIEL  D.  LORD, 
H.  J.  FAIRCHILD, 
WM.  ALEXANDER, 
HORACE  PORTER, 
C.  B.  ALEXANDER, 
GEO.  DE  F.  L.  DAY, 
J.  F.  DE  NAVARRO, 
JOSEPH  T.  Low, 
EDWARD  W.  SCOTT, 
CHARLES  S.  SMITH, 
GEORGE  H.  STUART,  \ 


A.  VAN  BERGEN, 
T.  DE  WITT  CUYLER 
OLIVER  AMES, 
EUSTACE  C.  FITZ, 
S.  H.  PHILLIPS, 
HENRY  R.  WOLCOTT, 
GUSTAV  G.  POHL, 
JOHN  A.  MCCALL, 
JAMES  H.  DUNHAM, 
DANIEL  R.  NOYES, 
WALDO  ADAMS. 


FIRST  EDITION. 


How  TO  VALUE  BONDS. 


PUBLISHED   UNDER  THE  AUSPICES  OF 

THE  EQUITABLE   LIFE  ASSURANCE  SOCIETY 


OF  NEW  YORK. 


HORATIO  J.  CROAD, 

ACTUARY,    ETC.,    16    AND     18     EXCHANGE     PLACE,    NEW    YORK. 


ALL  RIGHTS^  RESERVED. 


NEW  YORK: 
BURR     PRINTING     HOUSE, 

18  JACOB  STREET. 


• 


Entered  according  to  Act  of  Congress  in  the  year  1889,  by  Horatio  J.  Croad,  in  the  Office 
of  the  Librarian  of  Congress  in  Washington. 


A 


THE  publication  of  this  little  treatise  was  suggested  by  the  fact  that  there  have 
been  so  many  doubts  and  so  much  mystery  as  to  the  mode  of  valuing  bonds  mathe- 
matically, and  also  as  to  the  real  meaning  of  a  person  being  able  to  pay  a  certain 
price  for  a  bond  of  a  particular  denomination  in  order  to  realize  either  a  lower  or 
higher  rate  of  interest  on  the  investment  than  the  bond  calls  for. 

For  instance.  An  8$  $1,000  bond  having  5  years  to  run,  interest  payable  semi- 
annually  and  costing  $1,284.14  (market  price,  128.41),  is  said  to  realize,  at  the  rate  of 
2$  annually  or  i$  semi-annually  on  the  investment. 

The  following  will  explain  its  meaning : 

First.     The  investor  receives  the  semi-annual  interest  on  the  bond $    40.00 

ifi  on  the  investment  of  $1.284.14  is 12.84 

Difference $    27.16 


If  $27.16  is  set  aside  every  half  year  and  invested  at  2$  annually  (or 

i$  semi-annually),  it  would  in  5  years  amount  to $   284. 14 

To  which  add  the  face  value  of  the  bond 1,000.00 


The  original  amount  invested $1284. 14 

Second.    The  bond  at  maturity  is  worth  $1,000,  and  the  semi-annual 
interest  is $    40.00 

By  the  payment  of  $30.00  at  the  end  of  every  half  year  (interest  computed  at  \<jb 
semi-annually),  the  investor  can  borrow  at  the  time  the  bond  is  purchased  $284.14,  and 
at  the  end  of  5  years  the  debt  would  be  liquidated. 

So  that  the  investor  of  $  1,000  gets  semi-annually $    40.00 

Pays  out  for  the  $284.14 30.00 


\%  on  $i,ooo  is  the  difference , $     10.00 

Third.     A  4$  $1,000  bond  having  5  years  to  run,  interest  payable  semi-annually 
to  realize  4^^  on  the  investment,  is  said  to  be  worth  $977.83  (market  value,  97.78). 
That  is,  on  the  investment  of  $977.83  the  investor  receives  semi-annually. $     20.00 
An  investment  of   $22.17  ($1,000  minus  $977.83)  would  yield  every  six 

months  at  4^$  annually,  and  then  the  fund  would  be  exhausted $      2. 50 


Total  amount  received  semi-annually  .........................  $     22  .  50 

$22.50  is  21X%  on  $1.000  semi-annually,  or  4,^$  annually  on  the  investment. 


Fourth.     Or  2^%  on  the  investment  of  $977.8313  ....................  $     22.00 

Actual  semi-annual  interest  .....................  .  ..................       20.00 


Difference f $    2 .  oo 


If  the  investor  spend  $22.00  semi-annually  instead  of  $20.00  there  will  be  a  defi- 
ciency of  $2.00  every  six  months,  which,  had  it  been  invested  at  ^%%  annually  (2%'fa 
semi-annually),  it  would  in  5  years  have  amounted  to  $22. 17,  which  is  balanced  by  the 
difference  between  $1,000  received  at  the  maturity  of  the  bond  and  the  $977.83,  the 
amount  paid  for  it. 

Note. — The  reinvestments  are  made  at  the  rate  of  interest  to  be  realized.  The 
U.  S.  Treasury  Department,  Price,  and  others  have  adopted  this  method  as  per  letter 
in  possession  of  the  author  of  this  work  from  the  late  Actuary  Elliott  of  the  U.  S. 
Treasury,  and  the  tables  in  this  work  are  intended  for  the  valuation  of  bonds  according 
to  it. 


380357 


Example  I.  What  is  the  value  of  an  8$  bond  for  $1,000,  having  5  years  to  run, 
interest  payable  semi-annually  so  as  to  realize  2$  (\%  semi-annually  on  the  invest- 
ment) ? 


Semi-annual  interest  on  bond $40.00 

$40.00  every  half  year  for  5  years,  at  2%  per  annum,  amounts  to $  418 . 18 

Add..  .    1,000.00 


$1,418.18 


$1,418.18  due  in  5  years,  discounted  at  2$  per  annum  (\%  semi-annually), 

is $1,284.14 


51,284.14  is  the  present  value  of  the  bond — that  is,  $1.00  in  5  years,  at 
•zfo  per  annum  (interest  semi-annual),  amounts  to $  1.10462 


[,418.18  divided  by  1.10462 $1,284.14 


Example  II.  What  is  the  value  of  a  \%  bond  for  $1,000,  having  5  years  to  run, 
interest  payable  semi-annually,  so  as  to  realize  4X$  (2X$  semi-annually)  on  the  in- 
vestment ? 

Semi-annual  interest  on  bond $20.00 

$20.00  every  half  year  for  5  years,  at  4%%  per  annum,  amounts  to $    221 . 51 

Add..  1,000.00 


$1,221 .51 

Amount  of  $1.00  in  5  years  at  4%%,  interest  payable  semi-annually $    i  .2492 

$1,221.51  divided  by  1.2492 $   977.83 

$977.83  is  the  present  value  of  the  bond. 


ANOTHER  METHOD. 


A  much  more  simple  method  is  the  following  . 

Example  I.     (See  above.)     Semi-annual  interest  on  bond $    40.00 

"        to  be  realized. .  10.00 


Difference $     30-00 

So  that  a  price  is  to  be  paid  for  it  now  which  will  cause  a  loss  to  the  investor  of 
$30.00  every  six  months  out  of  the  $40.00  received. 

The  present  value,  then,  of  future  losses  will  be  the  premium  to  be  paid  on  the  bond. 
Referring  to  Table  I.,  page  10.     The  present  value  of  $1.00  for  every  half 
year  for  5  years,  at  2%  per  annum,  is  $9.4713.     This,  multiplied  by  30, 

gives  the  premium  on  the  bond $    284. 14 

Add..  1,000.00 


The  value  of  the  bond $1,284. 14 


PRC 
The  following  is  the  proof,  and  shows  t 
PresentValue,  $1,284.14,  5  yrs.  to  maturity. 
Add  i  %  f  or  6  mos     1  2.84 

)OF. 

he  values  every  six  months  to  maturity  : 
$1,145.61 
Add  i%                   11.46 

Deduct 

i  296.98 
40.00 

Deduct 
Add  \% 
Deduct 
Add  \% 
Deduct 
Add  \% 
Deduct 
Add  \% 
Deduct 

1,157.07 
40.00 

Add  \% 

1,256.98,  4^  "          " 
12.57 

1,1  17.07,  2  yrs.to  maturity. 
11.17 

Deduct 

1,269.55 
40.00 

1,128.24 
40.00 

Add  \<f0 

1,229.55,4     " 
12.30 

1,088.24,  i  X  " 
10.88 

Deduct 

1,241.85 
40.00 

1,099.12 
40.00 

Add  \% 

1,201.85,  3#" 

1  2.  02 

1,059.12,  i  year         " 
10.59 

Deduct 

1,213.87 
4O.OO 

1,069.71 
40.00 

Add  i% 

11.74 

1,029.71,  YL      "            " 

10.29 

Deduct 

1,185.61 
40.00 

1,040.00 
40.00 

Forward 

I,I45.6l,  2^"             " 

1,000.00  at  maturity. 

ANOTHE 
$1.00  every  six  months  for  five  years  at 
Dividing  the  premium,  $284.14  by  io.4< 
$27.16  is  the  semi-annual  Sinking  Func 
1%  per  annum,  and  will  at  the  matur 
$40.00  less  $27.16  is  $12.84. 
$12.84  is  the  net  interest  realized  on  the 
annually  on  the  investment,  or  2%  annually 
•  PROOF  BY  Si 
$27.16  end  of  *4  year. 
Add  \%                          .27 
27.16 

R  PROOF. 
z%  per  annum 

)22I     

amounts  to  $10.46221 

27.16 

to  be  set  asid 
ty  of  the  bond 

investment  se 
NKING  FUND. 
Add  \% 

Add  \% 

«                     M 

Add  \% 
Add  i* 
Add  i% 

e  and  improved  at 
amount  to        ....284.14 

ni-annually,  and  is  \%  semi- 

$138.53 
1.38 
27.16 

Add  \% 
Add  \% 

Add  \% 
Forward 

54.59      "      «    I         « 

•54 
27.16 

167.07  end  of  3  years. 
1.67 
27.16 

82.29  "   "  *  ^  yrs- 
.82 
27.16 

. 

195.90          "  3X  " 
1.96 
27.16 

110.27     "      "   2        " 
I.IO 
27.16 

225.02    "    "  4      " 
2.25 
27.16 

138.53      "      "   2^    " 

254.43     "     "  4^  " 
2.55 
27.16 

284.14    "    "  5      " 

Subtracting  these  respective  amounts  from  $1,284.14  and  the  results  will  be  the 
values  as  arrived  at  by  the  former  proof : 

$1,284.141688    *    *    $1,284.14,  5     years  to  maturity. 

1,284.14     "     $27.16    1,256.98  \V2         "  " 

1,284.14    "       54.59    1,229.55  4 

1,284.14    "      82.29    1,201.85  3/£         "  " 

1,284.14     "     110.27    i,i73-87  3 

1,284.14      "       138.53      1,145.61       2%  "  " 

1,284.14      "       167.07      1,117.07       2  "  " 

1,284.14      "       195.90      1,088.24       l%  "  " 

1,284.14     "     225.02    1,059.12     I     year  " 

1,284.14     "     254.43     1,029.71       X 
1,284.14     "     284.14    1,000.00    maturity. 
Being  the  same  results  as  by  the  former  proof. 

PROOF  BY  THESE  TABLES. 

Referring  to  Table  I.,  page  10. 

The  present  values  of  $1.00  every  six  months  for  5  years,  at  2%  per  annum,  are  as 
follows : 

5      years $94713° 

4X      "     8.56602 

4        "     7.65168 

3^      "     6.72819 

3         "     579548 

2^     "     4.85343 

2         "     3-90I97 

i%      "     2.94099 

I     year     1 .97040 

j£      "     99010 

Multiplying  these  respectively  by  $40.00  less  $10.00  ($30.00)  will  give  the  premiums, 
and  then  adding  $1,000  will  give  the  values,  as  follows  : 

5  years,  $284.14;  add  $1,000 $1,284.14 

4X       "        256.98     "          "  1,256.98 

4  "        229.55     "          »  1,229.55 

3X       "        201.84    "         "  1,201.84 

3          "        I73-87    "         "  1,173-87 

2%          "  I45.6I       "  "         I,I45.6l 

2  "  117.06      "  "         I,II7.06 

\yz    "     88.24  "     "   1,088.24 

I     year  59-J2     "         "      1,059.12 

X       "    **    29.71     "          "      1,029.71 

"          *      *     "          "      1,000.00 

NOTE. — There  is  a  variation  of  i  cent  occasionally  on  account  of  fractions. 


Treating  each  of  these  values  as  those  of  an  independent  bond  each  half  year,  the 
results  would  be  the  same,  but  the  Sinking  Funds  would  be  different,  and  as 
follows  : 

Present  value  of  a  bond  having  5  years  to  run $1,284.14 

"       "        "        "        4      "        "      1,229.55 

' '        "        3      "        "      1,173.87 

"  "          "  "  "  2        "  "         I,II7.O7 

"  "       "         "         "         I  year       "       1,059.12 


The  sinking  funds  for  these  are  as  follows  : 
5  year  bond,.  $40.00  less  $12.84            $27.16 
4    "        "           "        "       12.30              27.70 
3     "        "           "        "       11.74              28.26 
2     "        "           "        "       11.17              28.83 
I     "        "           "         "       10.59              29.41 

The  amounts  $12.84,  $12.30,  etc.,  are  obtained  by  taking  1%  of  the  values  of  the 
bonds  —  that  is, 
\%  on  $1,284.14            $12.84 
1,229.55               12.30 
1,173.87               11.74 
"        1,117.07               11.17 
"        1,059.12              IO-59 
• 

THE  MODE  OF  PROVING  TABLES  I.,  II.,  III.,  IV.,  V.,  VI.,  VII.,  VIII.,  IX.,  AND  X. 

For  instance.     The  present  value  of  $i 
annum  (\<fa  semi-annually),  is  $9.47130  (set 
$9.47130,  5  yrs. 
Add  \%                    9472 

.00  each  half  year  for  5  years,  at  1%  per 
:  Table  I.,  page  lo). 

$4.85343 
Add  i%                     4854 

9.56602 
Deduct                 1  .00 

4.90197 
Deduct                 i.oo 

8.56602,  \yz  " 

Add  \%                    8566 

3.901  97,  2  yrs. 
Add  i$                     3902 

8.65168 
Deduct                  i.oo 

3-94099 
Deduct                  i.oo 

7.65168,  4 
Add  i%                    7651 

2.94099,  \yz  " 

Add  i%                    2941 

7.72819 
Deduct                 i.oo 

2.97040 
Deduct                 i  .00 

6.72819,  3X  " 
Add  i$                     6729 

1.97040,  i  year 
Add  \%                     1970 

6.79548 
Deduct                 i.oo 

i  .99010 
Deduct                i.oo 

5-79548,  3     " 
Add  \%                    5795 

.99010,  j£    " 
Add  \%                     990 

5-85343 
Deduct                 i.oo 

I.OOOOO 

Deduct                i.oo 

Forward           4.85343  2j£  " 

*        * 

RULE   FOR  VALUING   BONDS. 

Find  the  difference  between  the  semi-annual  interest  on  the  bond  and 
the  interest  to  be  realized.     Multiply  it  by  the  present  value  of  $1.00  for 
every  half  year  during  the  term  of  the  bond  at  the  rate  to  be  realized.     If 
the  rate  to  be  realized  is  greater  than  that  of  the  bond,  subtract  the  result 
from  $1,000,  and  if  the  rate  to  be  realized  is  less  than  that  of  the  bond, 
add  it  to  $1,000.     The  amounts  thus  obtained  will  be  the  values  required. 
NOTE.—  Where  time  and  price  are  given,  the  rate  of  interest  realized  can  only 
be  approximately  ascertained. 

Example  III.     What  is  the  value  of  a  4$  bond  for  $1,000,  having  50  years  to  run, 
so  as  to  realize  ^%%  on  the  investment,  interest  payable  semi-annually  ? 


Semi-annual  interest  on  bond  ..........................................  $20.00 

"  "      to  be  realized  on  the  bond  .........................   22.50 


Difference $2.50 


Present  value  of  $1.00  for  every  half  year  for  fifty  years  at  the  rate  to  be 

realized  (4)4%  per  annum).     See  Table  VI $39.64174 

$39.64174  multiplied  by  2.50 $99.10 

As  the  rate  to  be  realized  is  greater  than  that  of  the  bond,  this  amount  has  to  be 
subtracted  from  $1,000. 

$1,000  minus  $99.10 $   900.90 


$900.90  is  the  value  of  the  bond,  or  market  value,  90.09. 


Example  IV.     What  is  the  value  of  the  bond  in  the  last  example  so  as  to  realize 
on  the  investment  ? 

Semi-annual  interest  on  bond $20 .  oo 

"  "       to  be  realized JO 


Difference $  2.50 


Present  value  of  $1.00  for  every  half  year  for  fifty  years  at  the  rate  to  be 

realized  (3%%  per  annum).     See  Table  IV $47.06147 

$47.06147  multiplied  by  2.50 $     117.65 


As  the  rate  to  be  realized  is  less   than   that  of  the  bond,  this  amount  has  to  be 
added  to  $  1,000. 

$1,000  plus  $117.65 $1,117.65 

$1,117.65  is  the  value  of  the  bond,  or  market  value,  111.77. 


NOTE. — Of  course  bonds  of  any  amount  would  be  dealt  with  as  in  the  foregoing  examples. 


Example  V.  What  are  the  values  of  an  8$  $1,000  bond,  having  50  years  to  run, 
so  as  to  realize  2,  2^,  2#,  2#,  3,  3#,  $#,  &,  4,  4#,  4#.  4#.  5.  S%>  SJA,  Stf,  6, 
6/£,  6^,  6%  and  7$  interest  payable  semi-annually  ? 

Referring  to  Tables,  the  present  values  of  $1.00  every  six  months  for  50  years,  at 
the  rates  required  to  be  realized,  are  as  follows  : 


• 

Difference  in 

Difference  in 

At 

Present  Value  of 
$1.00  every  half 
year  for  50  years. 

semi-annual 
interest  real- 
ized and  that 
to  be  real- 

At 

Present  Value  of 
$1.00  every  half 
year  for  50  years. 

semi-annual 
interest  real-, 
ized  and  that 
to  be  real- 

ized. 

ized. 

2_  % 

$63.02888 

$30.00 

4#* 

$38.07860 

$16.25 

59.84906 

28.75 

5 

36.61410 

15.00 

2>2 

56.90134 

27.50 

35.24058 

13-75 

2^ 

54.16588 

26.25 

\yz 

33-95I04 

12.50 

3 

51.62470 

25.00 

5\ 

32.73910 

11.25 

3* 

49.26150 

23-75 

6 

31.59891 

IO.OO 

47.06147 

22.50 

6X 

30.52513 

8.75 

3K 

45.01117 

21.25 

29.51288 

7.50 

4 

43-09835 

2O.OO 

6^ 

28.55768 

6.25 

41.31192 

18.75 

7 

27.65543 

5.00 

4/5 

39.64174 

17.50 

Multiplying  these  respective  amounts,  and  then  adding  $  1,000  to  each  result,  will 

give  the  respective  values. 

For  instance  •  At  2$  6302888x30    ...           $1890.87 

Add  i  .000.00 

$2890.87 

$2890.87  is  the  value  of  the  bond,  or  market  value,  289.09. 

Completing  the  operations  in  a  similar  manner,  and  the  following  are  the  results 

obtained  : 

Value  of  $1,000 

Market 

A  i 

Value  of  $i,ooo 

Market 

At 

bond. 

quotation. 

At 

bond. 

quotation. 

2      % 

$2,890.87 

289.09 

M% 

$1,618.78 

161.88 

** 

2,720.66 
2,564.79 

272.07 
256.48 

$ 

1,549.21 
1,484.56 

154.92 
148.46 

2|2 

2,421.85 

242.19 

S% 

1,424-39 

142.44 

3 

2,290.62 

229.06 

5% 

1,368.31 

136^3 

3X 

2,169.96 
2,058.88 

217.00 
205.89 

6 
6X 

1,267.10 

131.60 
126.71 

4 

1,956.49 
1,861.97 

195.65 
186.20 

6# 

1,221.35 
1,178.49 

122.14 
117.85 

1,774.60 

177.46 

7 

1,138.28 

113.83 

4/4 

1,693.73 

169.37 

• 

FIXED  RATES  FOR  SINKING  FUNDS,  ETC. 


There  are  many  advocates  in  this  country  and  in  Europe  of  a  fixed  rate 
of  interest  for  all  sinking  funds  (annuities  to  provide  for  difference 
between  par  value  and  cost  of  bonds).  Without  an  arbitrary  rate  no 
comparative  values  can  be  made.  Many  Railroad,  Banking,  Insurance 
and  other  corporations  have  a  regular  Sinking  Fund  account  on  their 
ledgers,  to  which  is  charged  or  credited  the  Sinking  Fund,  which  has  to 
be  set  aside  at  regular  periods,  and  credited  with  interest,  so  that  at  the 
bond's  maturity  there  will  not  only  be  realized  the  amount  which  the 
bond  calls  for,  but  there  will  also  be  a  fund  to  be  added  to  it  which  will 
make  it  up  to  its  original  cost.  Also  from  this  fund  can  be  used  in 
the  same  way  at  regular  periods  an  amount  which,  with  compounding 
interest,  would  have  amounted  to,  at  the  bond's  maturity,  the  difference 
between  cost  and  face  value. 


When  the  Sinking  Fund  (which  is  usually  at  3^  or  4$)  is  at  a  fixed 
rate,  the  method  of  arriving  at  the  bond's  value  is  as  follows  : 

Example  VI.  What  is  the  value  of  a  $%'/<>  $1,000  bond,  having  50 
years  to  run,  so  as  to  realize  3$  annually  on  the  investment,  interest 
payable  semi-annually,  and  the  Sinking  Fund  to  be  at  4$  per  annum  ? 

Difference  between  semi-annual  interest  realized  on  bond 

and  that  to  be  realized  ................................  $2.50 

Amount  of  $1.00  per  every  6  months  for  50  years  at  4%  per 

annum  ...............................................  $312.2323 

$312.2323  X  2.50  X    ioo  ................................  $78,058.08 

See  Table  XI. 
$100  -f  i^  ($312.2323)  ..................................  $568.34845 


$78,058.08  divided  by  568.34845 $137. 34 

Add TOOO.OO 


$1137.34  is  the  value  of  the  bond. 


PROOF. 

Semi-annual  Sinking  Fund  is — $  .44 

312.2323 

Net  semi-annual  interest,  $17.50  less  44  cents 17.06 

$17.06  is  T.Yz'fo  semi-annually  on  $1137.34,  or  3$  annually. 


CAR  TRUST,  BUILDING  LOAN  AND  INSTALMENT  PLAN  PROBLEMS. 


By  these  tables  can  also  be  solved  problems  such  as  the  following  : 
Example  VII.     A  person  borrowing  (say)  $5,000  wishes  to  pay  it  back 

(principal    and    interest)    in    (say)  fifty  equal   semi-annual  instalments. 

What   would  be  the  semi-annual  payment,  interest  computed  at  3^,  4 

and  ^/zfo   per  annum  ? 

Referring  to  Tables  III.   aud    V.,    the    present  values  of  $1.00  every 

half  year  for  25  years  (50  payments)  are 

At  3}^  ................................................  $33.14121 

'   4$  ..................................................    31.42361 

29.83440 


Dividing  $5,000  respectively  by  these  amounts,  and  the  following  are 
the  results  : 


At  3^$  ..................................................  $150.87 

"   4$  ....................................................      159-12 

"    4/^$  ..................................................      167.59 

So  that  a  person  borrowing  $5,000,  by  paying  half  yearly  $150.87  for  25 
years  pays  off  the  loan  and  also  interest  at  3/^$  per  annum,  and  similarly 
by  paying  the  other  amounts  the  interest  paid  is  at  4  and 


PROOF. 

$5,000  in  25  years,  at  $%%  per  annum  (interest  semi-annual- 

ly),  amounts  to $11,903.95 

$5,000  in  25  years,  at  4$  per  annum  (interest  semi-annually), 

amounts  to   i3>457-95 

$5,000  in  25  years,  at  4^$  per  annum  (interest  semi-annual- 
ly), amounts  to 15,2 10. 25 

and 

$150.87    every  half  year  for  25  years,  at  zY^%  Per  annum, 

amounts  to 1 1,903.95 

$159.12  every  half  year    for  25    years,  at  4$  per   annum, 

amounts  to i3>457-95 

$167.59  every  half  year  for  25  years,  at  4^2$  per  annum, 

amounts  to 15,210.25 


TABLE  I. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

nf 

At  rates  per  cent,  per  annum. 

OI 

years. 

i. 

i%. 

iK- 

*k- 

2. 

a#. 

# 

.99502 

•99379 

.99256 

•99133 

.99OIO 

.98888 

I 

1.98510 

1.98141 

1.97772 

i  .97405 

1  .97040 

1.96675 

-iX 

2.97025 

2.96289 

2.95556 

2.94826 

2.94099 

2-93374 

2 

3.95050 

3-93827 

3.92611 

3.91401 

3.90197 

3.88998 

2^ 

4.92587 

4.90760 

4.88944 

4.87138 

4.85343 

4.83558 

3 

5.89638 

5.87091 

5.84560 

5.82045 

579548 

5.77066 

3/2 

6.86207 

6.82823 

6.79464 

6.76129 

6.72819 

6.69534 

4 

7.82296 

7.77961 

7.73661 

7.69397 

7.65168 

*  7-60973 

4^ 

8.77906 

8.72508 

8.67158 

8.61856 

8.56602 

8.51395 

5 

9.73041 

9.66467 

9.59958 

9-53513 

947130 

9.40811 

5X 

10.67703 

10.59843 

10.52067 

10.44374 

10.36763 

10.29232 

6 

11.61893 

11.52639 

11.43491 

11.34448 

11.25508 

11.16669 

6^ 

12.55615 

12.44859 

12.34235 

12.23740 

12.13374 

12.03134 

7 

13.48871 

13.36506 

13.24302 

13.12258 

13.00370 

12.88637 

7/2 

14.41662 

14.27583 

14.13700 

14.00008 

13.86505 

13-73189 

8 

15-33993 

15.18095 

15.02431 

14.86997 

14.71787 

14.56800 

8^ 

16.25863 

16.08045 

15.90503 

15-73231 

15.56225 

15.39480 

9 

17.17277 

16.97436 

16.77918 

16.58717 

16.39827 

16.21241 

9X 

18.08236 

17.86272 

17.64683 

17.43462 

17.22601 

17.02093 

10 

18.98742 

18.74556 

18.50802 

18.27471 

18.04555 

17.82045 

iotf 

19.88798 

19.62291 

19.36280 

19.10752 

18.85698 

18.61107 

ii 

20.78406 

20.49482 

2O.2I  121 

19-93311 

19.66038 

19.39290 

»tf 

21.67568 

21.36131 

21.05331 

20.75153 

20.45582 

20.16604 

12 

22.56287 

22.22242 

21.88915 

21.56286 

21.24339 

20,93057 

12^ 

23.44564 

23.07818 

22.71876 

22.36715 

22.O23I6 

21.68659 

13 

24.32402 

23.92863 

23.54219 

23.16446 

22.79520 

22.43421 

I3# 

25.19803 

24-77379 

24-35949 

23.95485 

23.55961 

23-17351 

H 

26.06769 

25.61371 

25.17071 

24.73839 

24.31644 

23.90458 

HX 

26.93302 

26.44841 

25.97589 

25-51513 

25.06579 

24.62752 

15 

27.79405 

27.27792 

26.77508 

26.28514 

25.80771 

25-34242 

i5X 

28.65080 

28.10228 

27.56832 

27.04847 

26.54229 

26.04936 

16 

29.50328 

28.92152 

28.35565 

27.80517 

27.26959 

26.74844 

i6tf 

30-35I53 

29.73567 

29.13712 

28.55531 

27.98969 

27.43974 

17 

3I-I9555 

30.54477 

29.91278 

29.29895 

28.70267 

28.12336 

I7X 

32.03537 

31.34884 

30.68266 

30.03613 

29.40858 

28.79936 

18 

32.87102 

32.14791 

31.44680 

30.76692 

30.10750 

29.46785 

i8# 

33.70250 

32.94203 

32.20527 

31-49137 

30.79951 

30.12890 

19 

34.52985 

33-73121 

32.95808 

32.20954 

31.48466 

30.78260 

i9# 

35-35309 

34.51548 

33.70529 

32.92147 

32.16303 

31.42902 

20 

36.17223 

35.29489 

34.44694 

33.62723 

32.83469 

32.06825 

20^ 

36.98729 

36.06946 

35.18306 

34.32687 

3349969 

32.70037 

21 

37.79830 

36.83921 

35.9I37I 

35-02045 

34.I58II 

33-32546 

2I# 

38.60527 

37.60419 

36.63892 

35.70800 

34.8IOOI 

33.94360 

22 

39.40823 

38.36441 

37.35873 

36.38959 

35-45545 

34-55485 

22% 

40.20720 

39.11991 

38.07318 

37.06527 

36.09451 

35-15931 

23 

41.00219 

39.87072 

38.78231 

37.73509 

36.72724 

35-75705 

23/4 

41.79322 

40.61686 

39.48617 

38.39910 

37-35370 

36.34813 

24 

42.58032 

4I-35837 

40.18478 

39-05734 

37.97396 

36.93264 

24^ 

43.36350 

42.09528 

40.87820 

39.70988 

38.58808 

37.51064 

25 

44.14279 

42.82760 

41.56645 

40.35676 

39.19612 

38.08222 

TABLE  II. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

r\( 

At  rates  per  cent,  per  annum. 

OI 

years. 

I. 

I*. 

Ifr 

I*. 

2. 

9*. 

25X 

44.91820 

43-55538 

42.24957 

40.99803 

39.79814 

38.64743 

26 

45.68975 

44.27864 

42.92762 

41-63373 

40.39419 

39.20636 

26/2 

46.45746 

44.99741 

43.60061 

42.26392 

40.98435 

39-75907 

27 

47-22135 

457H7I 

44.26860 

42.88865 

41.56866 

40.30563 

*7X 

47.98145 

46.42157 

44.93161 

43-50795 

42.14719 

40.84612 

28 

48.73776 

47.12703 

45.58969 

44.12189 

42.71999 

41.38058 

28/2 

49.49031 

47.82810 

46.24287 

44-73050 

43.28712 

41.90911 

i  29 

50.239  I 

48.52482 

46.89118 

45.33382 

43.84863 

42.43175 

'  29^ 

50.98419 

49.21722 

47.53467 

45.93192 

44.40459 

42.94858 

30 

51.72556 

49.90531 

48.17337 

46.52483 

44.95504 

43.45966 

30/2 

52.46324 

50.58913 

48.80732 

47.11259 

45.50004 

43.96505 

3i 

53.19726 

51.26870 

4943654 

47-69526 

46.03964 

44.46482 

3'X 

53.92762 

51.94405 

50.06109 

48.27287 

46.57390 

44.95903 

32 

54.65435 

52.61  520 

50.68098 

48.84547 

47.10287 

45-44774 

32^ 

55-37746 

53.28219 

51.29626 

49.41311 

47.62661 

45.93102 

33 

56.09698 

53-94503 

51.90695 

49.97582 

48.14516 

46.40892 

33K 

56.81291 

54.60376 

52.51311 

50.53365 

48.65857 

46.88150 

34 

57.52529 

55.25839 

53-H475 

5  1  .08664 

49.16690 

47.34883 

34^ 

58.23411 

55.90896 

53.71191 

51.63484 

49.67020 

47.81096 

35 

58.93942 

56.55549 

54.30462 

52.17828 

50.16851 

48.26794 

35X 

59.64121 

57.19800 

54.89292 

52.71701 

50.66190 

48.71984 

36 

60.33951 

57.83652 

5547685 

53.25106 

51.15039 

49.16672 

36K 

61.03434 

58.47108 

56.05643 

53.78048 

5I-6340S 

49.60862 

37 

61.72571 

59.10169 

56.63169 

54-30531 

52.11292 

50.04561 

37X 

62.41365 

5972839 

57.20267 

54.82558 

52.58705 

50-47773 

38 

63.09815 

60.35120 

57.76940 

55.34I35 

53.05649 

50.90505 

38X 

63.77926 

60.97013 

58.33191 

55.85264 

53.52I27 

51.32762 

39 

64.45697 

61.58523 

58.89023 

56.35949 

53.98146 

51.74548 

39# 

65.13132 

62.19650 

5944440 

56.86195 

54-43709 

52.15869 

40 

68.80231 

62.80397 

59.99444 

57.36005 

54.88821 

52.56731 

40)4 

66.46996 

63.40768 

60.54039 

57.85383 

55.33486' 

52.97138 

4i 

67.13428 

64.00763 

61.08227 

58.34332 

55.77709 

53.37096 

4iX 

67.79531 

64.60385 

61.62012 

58.82857 

56.21494 

53.76609 

42 

68.45304 

65.19638 

62.15396 

59.30961 

56.64845 

54.15683 

42^ 

69.10750 

65.78522 

62.68384 

59.78648 

57.07768 

54-54322 

43 

69.75871 

66.37040 

63.20976 

60.25921 

57.50265 

54.92531 

43X 

70.40668 

66.95195 

6373!77 

60.72785 

57.92342 

55.303I5 

44 

71.05142 

67.52989 

64.24990 

61.19241 

58.34002 

55.67678 

44X 

71.69296 

68.10424 

64.76417 

61.65295 

58.75249 

56.04626 

45 

72.33130 

68.67502 

65.27461 

62.10949. 

59.16088 

56.41163 

45X 

72.96647 

69.24226 

65.78125 

62.56207 

59.56523 

56.77294 

46 

73.59847 

69.80597 

66.28412 

63.01073 

59-96557 

57.13022 

46K 

74-22734 

70.36618 

66.78324 

6345549 

60.36195 

5748353 

47 

74.85307 

70.92291 

67.27865 

63.89640 

60.75441 

57.83291 

47/2 

7547569 

71.47619 

67-77038 

64.33348 

61.14298 

58.17840 

48 

76.09522 

72.02602 

68.25844 

64.76677 

61.52770 

58.52005 

48K 

76.71166 

72.57245 

68.74287 

65.19631 

61.90862 

58.85790 

49 

77-32503 

73-11547 

69.22369 

65.62211 

62.28576 

59.19199 

49X 

77.93536 

73.655I3 

69.70093 

66.04423 

62.65917 

59.52237 

50 

78.54264 

74.19143 

70.  1  7462 

66.46268 

63.02888 

59.84906 

TABLE  TIL 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

At  rates  per  cent,  per  annum. 

years. 

.* 

.*. 

3- 

3*. 

,*. 

3* 

X 

.98765 

.98644 

.98522 

.98401 

.98280 

.98160 

I 

1.96312 

1.95949 

1.95588 

1.95229 

1  .94870 

1.94512 

u* 

2.92653 

2.91935 

2.91220 

2.90508 

2.89798 

2.89092 

2 

3.87806 

3.86619 

3-85438 

3.84263 

3.83094 

3.81931 

2^ 

4.81783 

4.80019 

4.78265 

4.76520 

4.74786 

4.73061 

3 

5.74601 

5.72152 

5.69719 

5.67301 

5.64900 

5.62514 

6.66273 

6.63035 

6.59821 

6.56631 

6.53464 

6.50320 

4 

7.56812 

7.52686 

7-48593 

7.44532 

7.40505 

7.36511 

4% 

8.46234 

8.41120 

8.36052 

8.31028 

8.26049 

8.21115 

5 

9-34553 

9-28355 

9.22219 

9.16141 

9.10122 

9.04162 

5X 

10.21780 

10.14407 

10.07112 

9-99893 

9.92749 

9.85680 

6 

11.07931 

10.99292 

10.90751 

10.82305 

10.73955 

10.65698 

6j£ 

11.93018 

11.83025 

H.73I53 

1  1  .63400 

11.53764 

11.44244 

7 

12.77055 

12.65623 

12.54338 

12.43198 

12.32201 

12.21344 

7/2 

13.60055 

13.47100 

I3-34323 

13.21720 

.  13.09288 

12.97024 

8 

14.42029 

14.27473 

14.13126 

13.98987 

13.85050 

13.71312 

8jS^ 

15.22992 

15.06755 

14.90765 

14.75018 

14.59508 

14.44233 

9f 

16.02955 

15.84962 

15.67256 

15-49833 

15.32686 

15.15811 

16.81931 

16.62108 

16.42617 

16.23452 

1  6.04606 

15.86073 

10 

17.59932 

17.38207 

17.16864 

16.95893 

16.75288 

16.55041 

I0# 

18.36969 

18.13275 

17.90014 

17.67177 

17-44755 

17.22739 

II 

19.13056 

18.87324 

18.62083 

18.37320 

18.13027 

17.89192 

II>£ 

19.88204 

19.60369 

19.33086 

19.06342 

18.80125 

18.54422 

12 

'20.62423 

20.32423 

20.03041 

19.74261 

19.46069 

19.18451 

12% 

21.35727 

21.03500 

20.71961 

20.41093 

20.10878 

19.81301 

13 

22.08125 

21.73613 

21.39863 

21.06856 

20.74573 

20.42995 

I3//2 

22.79630 

22.42775 

22".o6762 

21.71568 

21.37173 

21-03553 

14 

23.50252 

23.10998 

22.72672 

22.35246 

21.98695 

21.62997 

14/4 

24.20002 

23.78297 

23.37608 

22.97905 

22.59160 

22.21347 

15 

24.88891 

24.44683 

24.01584 

23.59562 

23.18585 

22.78623  - 

I5# 

25.56929 

25.10168 

24.64615 

24.20233 

23.76988 

23.34844 

16 

26.24127 

2574765 

25.26714 

24.79934 

24.34386 

23.90031 

i6j£ 

26.90496 

26.38486 

25.87896 

25.38680 

24.90797 

24.44203 

17 

27.56046 

27.01342 

26.48173 

25.96488 

25.46238 

24-97377 

!7X 

28.20786 

27.63346 

27.07560 

26.53370 

26.00725 

25.49572 

18 

28.84727 

28.24509 

27.66068 

27.09343 

26.54275 

26.00807 

1  8^ 

29.47878 

28.84842 

28.23713 

27.64422 

27.06904 

26.51099 

19 

30.10250 

29.44358 

28.80505 

28.18619 

27.58628 

27.00465 

i  /4 

30.71852 

30.03065 

29.36458 

28.71950 

28.09463 

27.48923 

20 

31-32693 

30.60977 

29.91585 

29.24428 

28.59423 

27.96489 

20^ 

31.92784 

31.18103 

30.45896 

29.76067 

29.08524 

28.43179 

21 

32.52132 

31-74454 

30.99405 

30.26880 

29.56780 

28.89010 

21^ 

33-I0748 

32.30041 

31.52123 

30.76881 

30.04207 

29.33998 

22 

33.68640 

32.84874 

32.04062 

31.26082 

30.50817 

29.78157 

22% 

34.25817 

33-38963 

32.55234 

31.74496 

30.96626 

30.21504 

23 

34.82288 

33-923I9 

33.05649 

32.22137 

31.41647 

30.64053 

23^ 

35.38062 

34-44951 

33.55319 

32.69015 

31.85894 

31.05819 

24 

35-93I48 

34.96869 

34.04255 

33.15144 

32.29380 

31.46816 

24X 

36.47554 

35-48083 

34.52468 

33.60535 

32.721  18 

31.87059 

25 

37.01288 

35.98602 

34.99969 

34.05201 

33.14121 

32.26561 

1 

TABLE  IV. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 
*t 

At  rates  per  cent,  per  annum. 

Of 

years. 

**. 

a#, 

3- 

a#< 

3#. 

3*. 

25X 

37.54358 

36.48436 

35.46767 

34.49152 

33-55401 

32-65336 

26 

38.06773 

36.97594 

35.92874 

34.92401 

33.95972 

33-03397 

26^ 

38.58542 

37.46086 

36.38300 

35-34957 

34.35845 

3340758 

27 

39.09671 

37-939I9 

36.83054 

35-76834 

3475032 

33-77431 

27^ 

39.60169 

38.41104 

37.27147 

36.18041 

35-13545 

34-13429 

28 

40.10043 

38.87649 

37.70588 

36.58589 

35-5!395 

34.48765 

28# 

40.59302 

39-33562 

38.13387 

36.98488 

35.88595 

34.83450 

29 

41.07952 

39-78853 

38.55554 

37-37750 

36.25155 

35-17497 

29^ 

41.56002 

40.23530 

38.97097 

37.76384 

36.61086 

35.50918 

30 

42.03459 

40.67600 

39.38027 

38.14400 

36.96399 

35-83723 

30^ 

42.50330 

41.11073 

3978352 

38.51808 

37-31104 

36.15924 

31 

42.96622 

41.53956 

40.  1  8080 

38.88618 

37-65213 

36.47533 

3»# 

43.42343 

41.96257 

40.57222 

39-24839 

37-98735 

36.78560 

32 

43.87499 

42.37985 

40.95785 

39.60481 

38.31681 

37.09016 

32X 

44.32098 

42.79147 

41-33779 

39-95553 

38.64060 

37-389" 

33 

44.76146 

43.I9750 

41.71211 

40.30065 

38.95882 

37.68256 

33X 

45.19651 

43-59803 

42.08089 

40.64025 

39.27157 

37.97062 

34 

45.62618 

43-99312 

42.44423 

40.97441 

39.57893 

38.25337 

34/2 

46.05055 

44.38286 

42.80220 

41-30323 

39.88102 

38.53091 

35 

46.46968 

44-76731 

43.I5487 

41.62680 

40.17790 

38.80335 

35^ 

46.88363 

45.14654 

43-50234 

41.94519 

40.46968 

39.07077 

36 

47.29247 

45.52064 

43.84467 

42.25849 

40.75645 

39-33327 

36X 

47.69627 

45.88965 

44.18194 

42.56678 

41.03828 

39-59094 

37 

48.09508 

46.25367 

44.51422 

42.87014 

41.31526 

39-84387 

37X 

48.48897 

46.61274 

44.84160 

43.16865 

41.58748 

40.09214 

38 

48.87800 

46.96694 

45.16414 

43.46238 

41.85502 

40.33584 

38X 

49.26222 

47-3  J634 

45.48191 

43-75  J42 

42.11795 

40.57506 

39 

49.64170 

47.66101 

45-79499 

44.03584 

42.37636 

40.80988 

39^ 

50.01649 

48.00099 

46.10343 

44.3I57I 

42.63033 

41.04037 

40 

50.38666 

48.33637 

46.40732 

44.59111 

42.87994 

41.26662 

40^ 

50.75225 

48.66719 

46.70672 

44.86210 

43.12524 

41.48871 

4i 

51.11334 

48.99353 

47.00170 

45.12875 

43-36633 

41.70671 

4»# 

51.46996 

49.3I544 

47.29231 

45.39II5 

43.60328 

41.92069 

42 

51.82219 

49.63299 

47.57863 

45.64935 

43.83614 

42.13074 

42^ 

52.17006 

49-94623 

47.86072 

45.90342 

44.06501 

42-33693 

43 

52.51364 

50.25522 

48.13864 

46.15342 

44.28993 

42.53931 

43X 

52.85298 

50.56002 

48.41246 

46.39943 

44.51099 

42.73798 

44 

53.18813 

50.86069 

48.68222 

46.64151 

44.72824 

42.93298 

44X 

53.51914 

51.15727 

48.94800 

46.87971 

44.94176 

43.12440 

45 

53.84606 

51.44984 

49.20985 

47.11411 

45.15161 

43.31229 

45^ 

54.16895 

5I-73844 

49.46784 

47.34476 

45-35785 

43-49673 

46 

54.48785 

52.02312 

49.72201 

47.57I7I 

45.56054 

43.67777 

46X 

54.80282 

52.30394 

49.97242 

4779505 

45-75974 

43.85548 

47 

55.11389 

52.58095 

50.21913 

48.01480 

45-95552 

44.02992 

47  X 

55.42113 

52.85421 

50.46220 

48.23105 

46.14793 

44.20115 

48 

55-72457 

53-12375 

50.70168 

48.44384 

46-33704 

44-36923 

48^ 

56.02427 

53-38965 

50.93761 

48.65322 

46.52288 

44-53421 

49 

56.32026 

53.65I93 

51.1  7006 

48.85926 

46.70554 

44.69616 

49X 

56.61261 

53.91066 

51.39907 

49.06200 

46.88505 

44.85512 

50 

56.90134 

54.16588 

51.62470 

49.26150 

47.06147 

45.01117 

TABLE  V. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 
^.f 

At  rates  per  cent,  per  annum. 

of 

years. 

4- 

4#. 

4#. 

4# 

5- 

5*. 

% 

.98039 

.97919 

.97800 

.97680 

.97561 

•97442 

I 

1.94156 

1.93801 

1-93447 

1.93094 

1.92742 

1.92392 

I# 

2.88388 

2.87688 

2.86990 

2.86295 

2.85602 

2.84913 

2 

3-80773 

3.79621 

3-78474 

3-77333 

3.76197 

3.75067 

2^ 

4.71346 

4.69641 

4.67945 

4.66259 

4.64583 

4.62916 

3 

5.60143 

5.57788 

5.55448 

5.53I23 

5.50813 

548517 

& 

6.47199 

6.44101 

6.41025 

6.37971 

6-34939 

6.31929 

4 

7.32548 

7.28618 

7.24718 

7.20851 

7.17014 

7.13207 

4X 

8.16224 

8.11376 

8.06571 

8.01808 

7.97087 

7.92407 

5 

8.98258 

8.92412 

8.86622 

8.80887 

8.75206 

8.69580 

5X 

9.78685 

9.71762 

9.64911 

9-58131 

9.51421 

94478o 

6 

iQ-57534 

10.49461 

10.41478 

10.33583 

10.25776 

10.18056 

6^ 

H.34837 

11-25543 

11.16360 

11.07285 

10.98318 

10.89458 

7 

12.10625 

12.00042 

11.89594 

11.79278 

1  1.69091 

II-59033 

7/2 

12.84926 

12.72991 

12.61217 

12.49600 

12.38138 

12.26829 

8 

I3.5777I 

13.44422 

i3-3I263 

13.18290 

13.05500 

12.92890 

8^ 

14.29187 

14.14367 

13.99768 

13-85387 

13.71220 

13.57262 

9 

14.99203 

14.82856 

14.66766 

14.50928 

14.35336 

14.19988 

9X 

1  5.67846 

15.49920 

15.32290 

15.14948 

14.97889 

14.81108 

10 

I6.35I43 

16.15589 

15.96371 

1577483 

15.58916 

15.40666 

ioX 

17.01121 

16.79892 

16.59043 

16.38567 

16.18455 

15.98700 

ii 

17.65805 

17.42856 

17.20335 

16.98234 

16.76541 

16.55250 

Hl/2 

18.29220 

18.04510 

17.80279 

17.56516 

17.33211 

I7-I0353 

12 

J8.9i393 

18.64881 

18.38904 

18.13447 

17.88499 

17.64047 

12% 

19.52346 

19.23996 

18.96238 

18.69057 

18.42438 

18.16367 

13 

20.12104 

19.81881 

19.52311 

I9.23377 

18.95061 

18.67349 

13* 

20.70690 

20.38562 

20.07150 

19.76436 

19.46401 

19.17027 

14 

21.28127 

20.94063 

20.60783 

20.28265 

1  9.96489 

I9.65435 

I4# 

21.84438 

2  1  .48409 

21.13235 

20.78891 

20.45355 

20.  1  2604 

15 

22.39646 

22.01625 

21.64533 

21.28343 

20.93029 

20.58566 

i5# 

22.93770 

22-53733 

22.14702 

21.76648 

21.39541 

21.03353 

16 

23-46833 

23.04757 

22.63767 

22.23832 

21.84918 

21.46995 

i6tf 

23.98856 

2354719 

23.H753 

22.69921 

22.29188 

21.89520 

I? 

24.49859 

24.03642 

23.58683 

23.14941 

22.72379 

22.30957 

I7# 

24.99862 

24.51546 

24.04580 

23.58917 

23.14516 

22.71335 

18 

25.48884 

24.98454 

24.49467 

24.01872 

23.55625 

23.10679 

i8# 

25.96945 

2544386 

24.93366 

24.43831 

23.95732 

23.49018 

19 

26.44064 

25.89362 

25.36299 

24.84817 

24.34860 

23.86375 

I9# 

26.90259 

26.33402 

25.78288 

25.24852 

24.73034 

24.22777 

20 

27.35548 

26.76526 

26.19352 

25-63958 

25.10277 

24.58248 

20^ 

27-79949 

27.18753 

26.59513 

26.02156 

25.46612 

24.92812 

21 

28.23479 

27.6OIOO 

26.98790 

26.39469 

25.82061 

25.26492 

2lX 

28.66156 

28.00588 

27-37203 

26.75916 

26.16644 

25.59310 

22 

29.07996 

28.40233 

27.74771 

27.11518 

26.50385 

25.91288 

22>£ 

29.49016 

28.79053 

28.11512 

27.46293 

26.83302 

26.22449 

23 

29.89231 

29.17066 

28.47444 

27.80262 

27.15417 

26.52813 

23K 

30.28658 

29.54287 

28.82586 

'  28.13443 

27.46748 

26.82400 

24 

30.67312 

29-90734 

29.16955 

28.45854 

27.77315 

27.1  1230 

24X 

31.05208 

30.26422 

29.50567 

28.77513 

28.07137 

27.39323 

25 

31.42361 

30.61368 

29.83440 

29.08437 

28.36231 

27.66697 

TABLE  VI. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 
/->* 

At  rates  per  cent,  per  annum. 

OI 

years. 

4- 

4* 

4* 

4* 

5- 

5#. 

25^ 

31.78785 

30.95587 

30.15589 

29.38645 

28.64616 

27.93371 

26 

32.14495 

31.29094 

30.47031 

29.68151 

28.92308 

28.19363 

26^ 

32.49505 

31.61903 

30.77781 

29.96973 

29.19325 

28.44690 

27 

32.83828 

31.94030 

31.07854 

30.25126 

29.45683 

28.69369 

27^ 

33-17479 

32-25489 

31.37265 

30.52626 

29.71398 

28.93417 

28 

33-50469 

32.56292 

3  1  .66030 

30.79488 

29.96486 

29.16849 

28^ 

33.82813 

32.86455 

31.94161 

31.05727 

30.20962 

29.39683 

29 

34.14523 

33.I5990 

32.21673 

3I-3I358 

30.44841 

29.61932 

29^ 

34.45610 

33-44911 

32.48580 

3L56393 

30.68137 

29.83612 

30 

34.76089 

33-73230 

32.74895 

31.80848 

30.90866 

30.04738 

3oX 

35.05969 

34.00960 

33.00631 

32.04736 

31.13040 

30.25323 

3i 

35-35264 

34.281  12 

33.25800 

32.28069 

3I-34673 

30.45382 

3'# 

35-63984 

34.54700 

33-50416 

32.50861 

3I-55778 

30.64927 

32 

35.92141 

34.80734 

33.74490 

32.73124 

31.76369 

30.83973 

32X 

36.19747 

35.06227 

33-98034 

32.94871 

31.96458 

31.02532 

33 

36.46810 

35-3II89 

34.21060 

33-16113 

32.16056 

31.20615 

33X 

36-73343 

35-55632 

3443580 

33-36863 

32-35177 

31-38237 

34 

36.99356 

35.79566 

34.65604 

33-57I3I 

32.53831 

3I-55407 

34X 

37.24859 

36.03002 

34.87H3 

33-76929 

32.72030 

31.72139 

35 

37.49862 

36.25951 

35.08208 

33.96268 

32.89786 

31.88442 

35# 

37-74374 

36.48422 

35.28810 

34.15158 

33.07108 

32.04328 

36 

37.98406 

36.70425 

3548959 

34.33609 

33.24008 

32.19808 

36X 

38.21967 

36.91971 

35.68664 

34-51633 

33-40495 

32.34893 

37 

38.45066 

37.13068 

35-87935 

34.69239 

33-5658I 

3249591 

37K 

38.67711 

37.33727 

36.06783 

34.86436 

33.72274 

32-63913 

38 

38.89913 

37-53955 

36.25215 

35.03234 

33-87584 

32.77869 

38X 

39.1  1680 

3773763 

36.43242 

35-I9643 

34.02521 

32.91468 

39 

39.330I9 

37.93158 

36.60873 

35-35670 

34.17094 

33-047I9 

39^ 

39-53940 

38.12150 

36.78115 

35-5I326 

34.31311 

33-17631 

40 

39-74451 

38.30746 

36.94978 

35.66619 

34.45182 

33-302I3 

40^ 

39.94560 

38.48956 

37.11470 

35.81557 

34.587H 

33-42473 

4i 

40.14275 

38.66787 

37-27599 

35-96I49 

34.71916 

33.54420 

<M# 

40.33603 

38.84247 

37-43373 

36.10402 

34.84796 

33.66061 

42 

40.52552 

39-oi343 

37.58800 

36.24324 

34.97362 

33-77404 

42X 

40.7  1  1  29 

39.  1  8084 

37.73888 

36.37923 

35.09621 

33-88457 

43 

40.89342 

39.34476 

37-88643 

36.51207 

35.21582 

33.99227 

43X 

41.07198 

39.50528 

38.03074 

36.64183 

35.33251 

34.09722 

44 

41.24704 

39.66245 

38.17187 

36-76857 

35-44635 

34.19948 

44^ 

41.41867 

39-81635 

38.30990 

36.89238 

35-55741 

34.29913 

45 

41.58693 

39.96705 

38.44489 

37.01331 

35-66577 

34.39623 

45X 

41.75189 

40.11462 

38.57691 

37.I3I44 

35-77I48 

34.49084 

46 

41.91362 

40.25911 

38.70602 

37.24683 

35.87462 

34.58304 

46^ 

42.07218 

40.40060 

38.83230 

37-35954 

35-97523 

34.67288 

47 

42.22762 

40.53914 

38.95579 

37.46964 

36.07340 

34.76042 

47X 

42.38002 

40.67480 

39.07657 

37.577i8 

36.16917 

34.84572 

48 

42.52943 

40.80764 

39.19469 

37.68223 

36.26261 

34-92883 

48X 

42-67592 

40.93771 

39.31021 

37.78484 

36.35376 

35-00983 

49 

42.81952 

41.06508 

39-4231  9 

37-88507 

36.44269 

35.08875 

49X 

42.96032 

41.18980 

39-53368 

37-98297 

36.52946 

35.16565 

50 

43-09835 

4L3"92 

39-64I74 

38.07860 

36.61410 

35.24058 

TABLE  VII. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

At  rates  per  cent,  per  annum. 

nf 

\JL 

years. 

5#. 

5#. 

6. 

6X- 

6£ 

6#. 

X 

•97324 

.97205 

.97087 

.96970 

.96852 

.96735 

I 

1  .92042 

1.91694 

i  -9  i  347 

1.91001 

1.90656 

1.90312 

1% 

2.84226 

2.83542 

2.82861 

2.82183 

2.81507 

2.80834 

2 

3-73943 

3.72824 

3.71710 

3.70601 

3.69498 

3.68401 

2^ 

4.61258 

4.59610 

4-57971 

4.56341 

4.54720 

4.53108 

3 

5.46237 

5-43971 

5.41719 

5.39482 

5-37259 

5.35050 

3^ 

6.28941 

6.25974 

6.23028 

6.20104 

6.17200 

6.14317 

4 

7.09431 

7.05686 

7.01969 

6.98282 

6.94625 

6.90996 

41A 

7.87768 

7.83169 

7.78611 

7.74092 

7.69612 

7.65171 

S 

8.64008 

8.58488 

8.53020 

8.47604 

8.42240 

8.36925 

S/2 

9.38207 

9.31701 

9.25262 

9.18889 

9.12581 

9.06336 

6 

10.10420 

10.02869 

9.95400 

9.88014 

9.80708 

9.7348i 

6^ 

10.80701 

10.72048 

10.63496 

10.55043 

10.46690 

10.38434 

7 

11.49101 

11.39293 

11.29607 

11.20042 

11.10596 

11.01266 

7/2 

12.15670 

12.04659 

n-93794 

11.83071 

11.72490 

1  1  .62047 

8 

12.80457 

12.68198 

12.56110 

12.44190 

12.32436 

12.20844 

8X 

1  3-435  1  1 

13.29962 

13.16612 

I3-03457 

12.90495 

12.77721 

9 

14.04877 

13.89999 

I3-7535I 

.  13.60928 

13.46726 

13-32741 

9>£ 

14.64600 

14.48359 

14.32380 

14.16658 

14.01188 

13.85964 

10 

15.22725 

15.05088 

14.87748 

14.70698 

H-53935 

14.37450 

ioX 

15.79295 

15.60231 

15.41502 

15.23101 

15.05021 

14.87256 

ii 

16.34350 

16.13833 

15.93692 

i5-739!7 

15.54500 

15-35435 

Hl/2 

16.87932 

16.65938 

16.44361 

16.23192 

16.02422 

15.82041 

12 

17.40080 

17.16586 

16.93554 

16.70974 

16.48834 

16.27125 

l2/2 

17.90832 

17.65819 

i7-4i3I5 

17.17308 

16.93786 

16.70738 

13 

18.40226 

18.13675 

17.87684 

17.62238 

I7-37323 

17.12927 

*3# 

18.88297 

18.60195 

18.32703 

18.05807 

17.79490 

17.53738 

14 

19-35083 

19.05414 

18.76411 

18.48055 

18.20329 

17.93217 

i4# 

19.80616 

19.49370 

19.18846 

18.89023 

18.59883 

18.31407 

15 

20.24930 

19.92097 

19.60044 

19.28749 

18.98192 

18.68350 

i5# 

20.68059 

20.33630 

20.00043 

19.67272 

I9-35295 

19.04087 

16 

21.10033 

20.74003 

20.38877 

20.04628 

19.71230 

19.38658 

i6# 

21.50883 

21.13247 

20.76579 

20.40851 

20.06034 

19.72099 

17 

21.90641 

21.51394 

21.13184 

20.75977 

20.39742 

20.04449 

I7X 

22.29334 

21.88475 

21.48722 

21.10038 

20.72389 

20.35743 

18 

22.66992 

22.24520 

21.83225 

21.43067 

21.04009 

20.66015 

i8# 

23.03642 

22.59558 

22.16724 

21.75095 

21.34634 

20.95298 

19 

23-393II 

22.93617 

22.49246 

22.06153 

2  1  .64294 

21.23626 

i9# 

23.74025 

23.26723 

22.80822 

22.36270 

21.93021 

21.51029 

20 

24.07810 

23.58905 

23.11477 

22.65474 

22.20843 

21.77537 

20^ 

24.40691 

23.90187 

23.41240 

22.93793 

22.47790 

22.03180 

21 

24.72692 

24.20595 

23.70136 

23.21254 

22.73889 

22.27985 

2I# 

25.03837 

24.50153 

23.98190 

23.47882 

22.99166 

22.51981 

22 

25-34I47 

24.78885 

24.25427 

23-73704 

23.23647 

22.75193 

22^ 

25.63647 

25.06814 

24.51871 

23-98743 

2347358 

22.97647 

23 

25-92357 

25-33963 

24-77545 

24.23024 

23.70323 

23.19369 

23X 

26.20299 

25.60353 

25.02471 

24.46568 

23.92564 

23.40381 

24 

26.47493 

25.86005 

25.26671 

24.69400 

24.14106 

23.60707 

24X 

26.73959 

26.10940 

25.50166 

24.91539 

24.34969 

23.80370 

25 

26.99717 

26.35179 

25.72976 

25.13008 

24.55176 

23-99390 

TABLE  VIII. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

f.e 

At  rates  per  cent,  per  annum. 

OI 

years. 

s#. 

5tf 

6. 

6# 

6tf. 

6Jf. 

25X 

27.24785 

26.58740 

25.95123 

25.33826 

24.74747 

24.17790 

26 

27.49183 

26.81643 

26.16624 

25.54013 

24.93702 

24-35589 

26X 

27.72927 

27.03906 

26.37499 

2573588 

25.12060 

24.52806 

27 

27.96036 

27.25546 

26.57766 

25.92570 

25.29840 

24.69462 

27X 

28.18527 

27.46582 

26.77443 

26.10977 

25.47060 

24.85574 

28 

28.4041  5 

27.67030 

26.96546 

26.28826 

25-63739 

25.01  160 

-  28^ 

28.61718 

27.86906 

27.15094 

26.46135 

25.79892 

25.16237 

29 

28.82451 

28.06227 

27.33101 

26.62918 

25-95537 

25.30822 

29X 

29.02628 

28.25008 

27.50583 

26.79194 

26.10690 

25.44930 

30 

29.22266 

28.43264 

27.67556 

26.94976 

26.25366 

25.58578 

3oX 

29.41378 

28.61010 

27.84035 

27.10279 

26.39579 

25.71781 

3i 

29.59979 

28.78260 

28.00034 

27.25119 

26.53346 

25.84552 

3'X 

29.78082 

28.95028 

28.15567 

27.39510 

26.66679 

25.96906 

32 

29.95700 

29.11328 

28.30648 

27.53464 

26.79592 

26.08857 

32^ 

30.  1  2846 

29.27171 

28.45289 

27.66995 

26.92099 

26.20418 

33 

30-29534 

2942573 

28.59504 

27.80117 

27.04212 

26.31602 

33X 

30-45775 

29-57543 

28.73305 

27.92841 

27.15944 

26.42420 

34 

30.61582 

29.72095 

28.86704 

28.05179 

27.27306 

26.52885 

34X 

30.76965 

29.86241 

28.99712 

28.17143 

27.38311 

26.63009 

35 

30.91937 

29.99991 

29,12342 

28.28745 

27.48970 

26.72802 

35X 

31.06508 

3013357 

29.24604 

28.39995 

27.59293 

26.82275 

36 

31.20689 

30.26350 

29.36509 

28.50904 

27.69291 

26.91439 

36X 

3  *  -3449  i 

30.38979 

29.48067 

28.61483 

27-78974 

27.00304 

37 

3I-47923 

30.51255 

29.59288 

28.71741 

27.88352 

27.08879 

37X 

31.60995 

30.63189 

29.70183 

28.81688 

27.97436 

27.17174 

38 

3I-737I8 

30.74789 

29.80760 

28.91334 

28.06233 

27.25199 

38X 

31.86100 

30.86064 

29.91029 

29.00687 

28.14754 

27.32961 

39 

31.98151 

30.97025 

30.00999 

29.09758 

28.23006 

27.40470 

39X 

32.09880 

31.07679 

30.10679 

29.18553 

28.30999 

27-47734 

40 

32.21294 

31.18035 

30.20076 

29.27081 

28.38740 

27.54761 

4oX 

32.32403 

31.28103 

30.29200 

29-35352 

28.46237 

27.61559 

4i 

32.43214 

31.37888 

30.38059 

2943371 

28.53498 

27.68134 

4iX 

32.53737 

31.47400 

30.46659 

29.51148 

28.60531 

27-74495 

42 

32.63977 

31.56647 

30.55009 

29.58689 

28.67342 

27.80648 

42^ 

32-73944 

31-65635 

30.63115 

29.66001 

28.73939 

27.86600 

43 

32.83644 

3I-74372 

30.70986 

29.73092 

28.80329 

27.92358 

43^ 

32.93084 

31.82864 

30.78627 

29.79968 

28.86517 

27.97928 

44 

33.02271 

3i'.9ii20 

30.86045 

29.86636 

28.92510 

28.03316 

44K 

33-11213 

31.99144 

30.93248 

29.93102 

28.98315 

28.08528 

45 

33-I99I5 

32.06945 

31.00241 

29.99371 

29.03937 

28.13570 

45X 

33-28385 

32.14527 

31.07030 

30.05451 

29.09382 

28.18448 

46 

33.36628 

32.21897 

31.13621 

30.11346 

29.14656 

28.23166 

46X 

33.44650 

32.29062 

31.20021 

30.  1  7063 

29.19764 

28.27730 

47 

33-52457 

32.36026 

31.26234 

30.22607 

29.24710 

28.32145 

47^ 

33.60056 

3242796 

31.32266 

30.27982 

29.29502 

28.36416 

48 

33-6745  I 

3249376 

31.38122 

30.33195 

29.34142 

28.40548 

48^ 

33-74648 

32.55773 

31.43808 

30.38249 

29.38636 

28.44544 

49 

33.81652 

32.61990 

31.49328 

3043151 

29.42989 

28.48410 

49^ 

33.88469 

32.68034 

31.54687 

30.47904 

29.47205 

28.52150 

50 

33-95  104 

32.73910 

31.59891 

30.52513 

29.51288 

28.55768 

TABLE  IX. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 
t 

At  rates  per  cent,  per  annum. 

of 
years. 

7- 

rA- 

8. 

Btf. 

9- 

10. 

'/* 

.96618 

.96386 

.96154 

•95923 

•95694 

.95238 

I 

1  .89969 

1.89287 

1.88609 

1.87936 

1.87267 

1.85941 

I# 

2.80164 

2.78831 

2.77509 

2.76198 

2.74896 

2.72325 

2 

3.67308 

3-65138 

3.62990 

3.60861 

3-58753 

3-54595 

2^ 

4.51505 

4.48326 

4.45182 

4.42073 

4.38998 

4.32948 

3 

5-32855 

5.28507 

5.24214 

5-19974 

5.15787 

5.07569 

3* 

6.11454 

6.05790 

6.00205 

5.94699 

5.89270 

5.78637 

4 

6.87396 

6.80280 

6.73275 

6.66378 

6.59589 

6.46321 

4X 

7.60769 

7.52077 

7-43533 

7-35I35 

7.26879 

7.10782 

5 

8.31661 

8.21279 

8.11090 

8.01089 

7.91272 

7.72173 

5X 

9.00155 

8.87980 

8.76048 

8.64354 

8.52892 

8.30641 

6 

9-66334 

9.52269 

9.38507 

9.25039 

9.11858 

8.86325 

6X 

10.30274 

10.14236 

9.98565 

9.83251 

9.68285 

9-39357 

7 

10.92052 

10.73962 

10.56312 

10.39090 

10.22283 

9.89864 

7/2 

11.51741 

11.31530 

11.11839 

10.92652 

10.73955 

10.37966 

8 

12.09412 

11.87017 

11.65230 

11.44031 

11.23401 

10.83777 

8X 

12.65132 

12.40498 

12.16567 

H-933I5 

11.70719 

11.27407 

9 

1  3-  tf968 

12.92046 

12.65930 

12.40590 

12.15999 

11.68959 

9^ 

13.70984 

1341731 

I3.I3394 

12.85938 

12.59329 

12.08532 

10 

14.21240 

13.89620 

I3.59033 

I3-29437 

13.00794 

12.46221 

10^ 

14.69798 

14-35779 

14.02916 

13.71162 

13.40472 

12.82115 

II 

15.16713 

14.80269 

14.45112 

14.11187 

13.78442 

13.16300 

n% 

15.62041 

15-23151 

14.85684 

14.49580 

14.14777 

13.48857 

12 

16.05837 

15.64482 

15.24696 

14.86407 

14.49548 

13.79864 

I2# 

16.48152 

16.04320 

15.62208 

15.21734 

14.82821 

14.09394 

13 

16.89035 

16.42719 

15.98277 

15.55620 

15.14661 

14.37518 

I3tf 

17.28537 

16.79729 

16.32959 

15.88124 

15.45130 

14.64303 

14 

17.66702 

17.15401 

16.66306 

16.19304 

15.74287 

14.89813 

I4# 

18.03577 

17.49784 

16.98372 

16.49212 

16.02189 

15.14107 

15 

18.39205 

17.82925 

17.29203 

16.77902 

16.28889 

I5.37245 

I5# 

18.73628 

18.14867 

17.58849 

17.05421 

16.54439 

15.59281 

16 

19.06887 

18.45655 

17.87355 

17.31819 

16.78889 

15.80268 

1  6^ 

19.39021 

18.75330 

18.14765 

17.57140 

17.02286 

16.00255 

17 

19.70069 

19-03933 

18.41120 

17.81430 

17.24676 

16.19290 

i7# 

20.00066 

19.31501 

18.66461 

18.04729 

17.46101 

16.37419 

18 

20.29050 

19.58074 

18.90828 

18.27078 

17.66604 

16.54685 

i«# 

20.57053 

19.83685 

19.14258 

18.48516 

17.86224 

16.71129 

19 

20.84109 

20.08371 

19.36787 

18.69080 

18.04999 

16.86789 

19^ 

21.10250 

20.32165 

19.58449 

18.88806 

18.22966 

17.01704 

20 

21.35507 

20.55099 

19.7927^7 

19.07727 

18.40158 

17.15909 

20>£ 

21.59911 

20.77204 

19.99305 

19.25878 

18.56611 

17.29437 

21 

21.83488 

20.98510 

20.18563 

19.43288 

18.72355 

17.42321 

2I# 

22.06269 

21.19046 

20.37080 

19.59988 

18.87421 

17.54591 

22 

22.28279 

21.38839 

20.54884 

19.76008 

19.01838 

17.66277 

22^ 

22.49545 

21.57917 

20.72004 

I9-91375 

19.15635 

17.77407 

23 

22.70092 

21.76306 

20.88465 

20.06115 

19.28837 

17.88007 

23X 

22.89944 

2  1  .94030 

21.04294 

20.20254 

19.41471 

17.98101 

24 

23.09125 

22.IIII3 

21.19513 

20.33817 

19.53561 

18.07716 

24^ 

23.27657 

22.27579 

21.34147 

20.46827 

19.65130 

18.16872 

25 

23.45562 

22.43449 

21.48219 

20.59306 

19.76201 

18.25592 

TABLE  X. 


PRESENT  VALUE  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 
^t 

At  rates  per  cent,  per  annum. 

01 
years. 

7- 

1%. 

8. 

SJ*. 

9- 

10. 

^A 

23.62862 

22.58746 

21.61749 

20.71277 

19.86795 

18.33898 

26 

23-79577 

22.73490 

21.74758 

20.82760 

I9.96933 

18.41807 

26X 

23.95726 

22.87702 

21.87268 

20.93774 

20.06634 

18.49340 

27 

24.11330 

23.01399 

21.99296 

21.04340 

20.15918 

18.56514 

27X 

24.26405 

23.14602 

22.10861 

21.14474 

20.24802 

18.63347 

28 

24.40971 

23.27327 

22.21982 

21.24196 

20.33303 

18.69854 

28>/2 

24.55045 

23-39592 

22.32675 

21.33521 

20.41439 

18.76052 

29 

24.68642 

23.51414 

22.42957 

21.42467 

20.49224 

18.81954 

29^ 

24.81780 

23.62809 

22.52843 

21.51047 

20.56673 

18.87575 

3° 

24.94474 

23.73792 

22.62349 

21.59278 

20.63802 

18.92929 

30^ 

25.06738 

23.84377 

22.71490 

21.67173 

20.70624 

18.98027 

3i 

25.18587 

23.94581 

22.80278 

21.74746 

20.77152 

19.02883 

y% 

25.30036 

24.04415 

22.88729 

21.82011 

20.83399 

19.07508 

32 

25.41098 

24.13894 

22.96855 

21.88979 

20.89377 

I9.II9I2 

32^ 

25.51785 

24.23030 

23.04668 

21.95663 

20.95098 

I9.l6l07 

33 

25.6211  1 

24-31837 

23.12181 

22.02075 

21.00572 

I9.2OIO2 

33^ 

25.72088 

24.40324 

23.19405 

22.08226 

21.05811 

19.23907 

34 

25.81728 

24.48505 

23.26351 

22.14125 

21.10824 

19.27530 

34^ 

25.91041 

24.56391 

23-33030 

22.19784 

21.15621 

19.30981 

35 

26.00040 

24.63991 

23.39452 

22.25213 

21.  2021  1 

19.34268 

35X 

26.08734 

24.71317 

23.45627 

22.30420 

21.24604 

I9.37398 

36 

26.17134 

24-78378 

23.51564 

22.35415 

2I.288o8 

I9-40379 

36K 

26.25251 

24.85183 

23.57273 

22.40206 

21.32830 

I9432I8 

37 

26.33092 

24.9I743 

23.62763 

22.44802 

2  1  .36680 

1945922 

37X 

26.40669 

24.98065 

23.68041 

22.49211 

21.40363 

1948497 

33 

26.47989 

25.04159 

23.73116 

22.53439 

21.43888 

19.50949 

38X 

26.55062 

25.10033 

2377996 

22.57496 

21.47262 

19.53285 

39 

26.61896 

.  25.15695 

23.82689 

22.61387 

21.50490 

19.55510 

39X 

26.68498 

25.21152 

23.87201 

22.65119 

21-53579 

19.57628 

40 

26.74878 

25.26411 

23.91539 

22.68700 

21.56534 

19.59646 

40^ 

26.81041 

25.31481 

23.95711 

22.72134 

21.59363 

19.61568 

4i 

26.86996 

25.36367 

23.99722 

22.75428 

2I.62O7O 

1  9-63398 

4i# 

26.92750 

25.41076 

24.03579 

22.78588 

21.64660 

19.65141 

42 

26.98309 

25.45616 

24.07287 

22.81619 

21.67139 

19.66801 

42^ 

27.03681 

25.49991 

24.10853 

22.84527 

21.69511 

19.68382 

43 

27.08870 

25.54208 

24.14282 

22.87316 

21.71781 

19.69887 

43X 

27.13884 

25.58273 

24.17579 

22.89991 

21-73953 

I97I32I 

44 

27.18729 

25.62191 

24.20749 

22.92558 

21.76032 

19.72687 

44^ 

27.23409 

25.65967 

24.23797 

22.95019 

2I.7802I 

19.73987 

45 

27.27932 

25.69607 

24.26728 

22.97381 

21.79924 

1975226 

45  % 

27.32301 

25.73115 

24.29546 

22.99646 

21.81746 

19.76406 

46 

27.36523 

25.76497 

24-32256 

23.01818 

21.83489 

1977529 

46X 

27.40602 

25.79756 

24.34861 

23-03903 

21.85156 

19.78599 

47 

27.44543 

25.82897 

24.37367 

23.05902 

21.86753 

19.79618 

47^ 

27.48351 

25.85925 

24.39776 

23.07819 

21.88280 

19.80589 

48 

27.52030 

25.88843 

24.42092 

23.09659 

21.89742 

19.81513 

48^ 

27.55584 

25.91656 

24.44319 

23.11423 

2I.9II4O 

19.82394 

49 

27.59018 

25.94367 

24.46461 

23.13116 

21.92479 

19.83232 

49X 

27.62337 

25.96981 

24.48520 

23.14740 

21.93760 

19.84030 

50 

27.65543 

25-99499 

24.50500 

23.16297 

21.94985 

19.84791 

TABLE  XI. 


AMOUNT  OF  ONE  DOLLAR  EVERY  HALF  YEAR. 

No. 

At  rates  per  cent,  per  annum. 

No. 

At  rates  per  cent,  per  annum. 

nf 

nf 

UI 

years. 

3#. 

4- 

Ui 

years. 

3/2. 

4- 

% 

I.OOOOO 

I.OOOOO 

25^ 

81.28301 

87.27099 

I 

2.01750 

2.O2OOO 

26 

8370547 

90.01641 

iK 

3.05281 

3.06040 

26^ 

86.17031 

92.81674 

2 

4.10623 

4.12161 

27 

88.67829 

95.67307 

2^ 

5.17809 

5.20404 

27X 

91.23016 

98.58653 

3 

6.26871 

6.30812 

28 

93.82669 

101.55826 

3/2 

7.37841 

743428 

28/2 

96.46866 

104.58943 

4   , 

8.50753 

8.58297 

29 

99.15686 

107.68122 

4^ 

9.65641 

975463 

29X 

101.89210 

110.83484 

5 

10.82540 

10.94972 

30 

104.67522 

114.05154 

5X 

12.01484 

I2.I6872 

30^ 

107.50703 

117.33257 

6 

13.22510 

I34I209 

31 

110.38841 

120.67922 

6^ 

14.45654 

14.68033 

3»# 

113.32020 

1  24.0928  1 

7 

1  5.70953 

15-97394 

32 

116.30331 

127.57466 

7K 

16.98445 

17.29342 

32X 

119.33861 

131.12615 

8 

18.28168 

18.63929 

33 

122.42704 

134.74868 

8/2 

19.60161 

2O.OI2O7 

33/2 

125.56951 

138.44365 

9 

20.94463 

21.41231 

34 

128.76698 

142.21252 

9/2 

22.31117 

22.84056 

34X 

132.02040 

146.05677 

10 

23.70161 

24.29737 

35 

I35-33076 

I49-97791 

10^ 

25.11639 

25.78332 

3S/2 

138.69905 

153-97747 

ii 

26.55593 

27.29898 

36 

142.12628 

1  58.05702 

n/2 

28.02065 

28.84496 

36K 

145.61349 

162.21816 

12 

29.51102 

30.42186 

37 

149.16173 

166.46252 

I2# 

31.02746 

32.03030 

37/2 

152.77206 

170.79177 

13 

32.57044 

33.67091 

38 

156.44557 

175.20761 

I3# 

34.14042 

35-34432 

3*/2 

160.18336 

179-71176 

14 

35.73788 

37.05121 

39 

163.98657 

184.30599 

I4# 

37.36329 

38.79223 

391A 

167.85634 

188.99211 

15 

39.01715 

40.56808 

40 

171.79382 

193.77196 

JStf 

40.69995 

42.37944 

40^ 

175.80022 

198.64740 

16 

42.41220 

44.22703 

4i 

179.87672 

203.62034 

i6tf 

44.15441 

46.11157 

4U* 

184.02456 

208.69275 

I? 

45.92712 

48.03380 

42 

188.24499 

213.86661 

I7# 

47.73084 

49.99448 

42^ 

192.53928 

219.14394 

18 

49.56613 

51-99437 

43 

196.90872 

224.52682 

1  8% 

51.43354 

54.03425 

43/2 

201.35462 

230.01735 

19 

53.33362 

56.11494 

44 

205.87833 

235.61770 

I9# 

55.26696 

58.23724 

44/2 

210.48120 

241.33005 

20 

57.23413 

60.40198 

45 

215.16462 

247.15666 

20# 

59-23573 

62.61002 

45X 

219.93000 

253-09979 

21 

61.27236 

64.86222 

46 

224.77877 

259.16178 

2I# 

63.34462 

67.15947 

46^ 

229.71240 

265.34502 

22 

65.45315 

69.50266 

47 

23473237 

271.65192 

22^ 

67.59858 

71.89271 

47/2 

239.84018 

278.08496 

23 

69.78156 

74.33056 

48 

245-03739 

284.64666 

23^ 

72.00274 

76.81718 

48/2 

250.32554 

29I-33959 

24 

74.26278 

79-35352 

49 

255.70624 

298.16638 

24X 

76.56238 

81.94059 

49X 

261.18110 

305.12971 

25 

78.90222 

84.57940 

50 

266.75177 

312.23230 

WORKS    BY   THE  SAME   AUTHOR. 


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